This invention relates generally to estimating an unknown, random parameter in a linear system in the minimum mean-square-error (MSE) sense, and adapting the estimator according to gradual changes in the system. It also relates to the application of estimation algorithms to digital radio communications, more particularly to implementation of low-complexity adaptive Linear Minimum Mean Square Error (LMMSE) wireless terminal receivers for, by example, Code Division, Multiple Access (CDMA) systems, including Wideband CDMA (WCDMA) systems.
The capacity of WCDMA systems is inherently interference limited. Users are separated by spreading codes which are orthogonal to one other. However, this orthogonality is lost at the receiver when there is multipath propagation in the channel that results in multiple-access interference. This interference is particularly severe for high data rate users that use very short spreading codes. Moreover, neighboring cells in a WCDMA system use the same frequency band, which results in significant inter-cell interference. The currently used CDMA receiver is the well-known RAKE-type. However, the use of the RAKE receiver is optimal only when there is no multipath propagation and the interference is xe2x80x9cwhitexe2x80x9d. Unfortunately, such conditions occur only rarely, thus making the RAKE a sub-optimal receiver.
The RAKE receiver used for WCDMA terminal receivers has no capability to reduce the interference caused by multipath propagation, and furthermore it cannot utilize the structure of the interference, i.e. its spatial and time-correlation properties. In a highly loaded cell, or with strong interference from neighboring cells, RAKE receiver does not function properly. Furthermore, if multiple wireless terminal antennas are used the RAKE receiver cannot intelligently direct the beam of the antenna array so that the signal-to-interference-plus-noise ratio (SINR) would be maximized.
The most optimum linear receiver, in the minimum mean-square-error (MMSE) sense, is well-documented in the literature, but too complex to be implemented in most applications.
In the literature, almost all algorithms used for finding the LMMSE solution are either too complex to implement in a practical receiver, and/or require a suitable training sequence. However, a suitable training sequence is not present in the third generation CDMA systems.
One problem that is common to most adaptive algorithms is that they are designed to operate on the symbol level. However, due to the long scrambling codes used in the WCDMA system the symbol level algorithms do not function properly. This is due to the fact that the scrambling code makes the signal non-cyclostationary on the symbol level. In other words, scrambling randomizes the signal correlation properties, thereby making adaptation impossible.
This problem can be avoided when the filter is designed to operate on the chip level, as opposed to the symbol level. However, due to the lack of a suitable training sequence on the chip level, the adaptation algorithm must be blind. Only a few practical algorithms for this purpose have thus far been developed or proposed.
One improved adaptive algorithm known to the inventors is the so-called Griffiths"" algorithm. This algorithm uses the channel impulse response to train the filter. However, training is still required, and the adaptation time may not be optimum for all applications.
It is a first object and advantage of this invention to provide an adaptive filter that eliminates the requirement to multiply by the inverse of the covariance matrix.
It is a further object and advantage of this invention to provide an adaptive filter that has computation requirements that are suitable for use in a wireless terminal, such as a WCDMA terminal, that employs one or more antennas.
It is another object and advantage of this invention to provide an adaptive finite impulse response (FIR) filter that does not require the use of a training sequence, and that is suitable for use in a wireless terminal, such as a WCDMA terminal, employing at least one reception antenna.
The foregoing and other problems are overcome and the foregoing objects and advantages are realized by methods and apparatus in accordance with embodiments of this invention.
This invention provides an algorithm that is embodied as an adaptive linear finite impulse response (FIR) filter which can be applied to determine a linear minimum mean-square-error (LMMSE) estimate of unknown, random parameters. Whereas the direct computation of the LMMSE solution is very complex and requires inversion of a large matrix, the complexity of the adaptive algorithm of this invention is of the order of the well known and significantly less complex Least Mean Square (LMS) algorithm.
The presently preferred adaptive FIR filter is blind, i.e., it does not require any training for the adaptation, which makes it applicable in, by example, WCDMA downlink receivers with one or multiple antennas. It is shown that the performance of the adaptive WCDMA terminal receiver is superior to the currently used RAKE receiver.
In general, the invention provides an adaptive algorithm which can be used to derive a linear filter which minimizes the mean-square-error of the estimate of some unknown parameter such as, but not limited to, a transmitted data symbol. Due to the adaptive processing, the high computational complexity required by the conventional direct solution for the optimal filter is avoided. The algorithm is applicable for use in advanced third generation wireless terminal receivers, as it does not require any training for the adaptation.
The adaptive algorithm in accordance with the teachings herein can be used to find a linear MMSE (LMMSE) solution with low computational requirements. When applied to WCDMA receivers, the adaptive LMMSE algorithm in accordance with these teachings equalizes the channel so that the interference from other users is minimized. In addition, due to the inherent whitening operation performed by the adaptive filter, the interference from neighboring cells is effectively suppressed. At the same time, the adaptive receiver is able to (near-)optimally perform beam steering in the case of a multi-antenna receiver.
Performance results show that the adaptive LMMSE receiver clearly outperforms the conventional RAKE receiver. The improved performance can be used to increase the reception reliability of the wireless terminal receiver, especially in severe interference conditions, or to increase the cell coverage, or the capacity of the system.
Unlike the Griffiths"" algorithm approach, in the adaptive algorithm of this invention the LMMSE estimator is divided into a blind adaptive filter and a filter matched to the channel impulse response and to the spreading code of the desired user. Thus no training is required at all.
In the case of significant multipath propagation, or very short spreading codes (high data rates), or a highly loaded home cell, or high interference from a neighboring cell, the adaptive receiver in accordance with this invention is shown to be superior to the conventional RAKE receiver.
The adaptive filter can, however, be used prior to a RAKE receiver, thereby causing the overall receiver to function as an adaptive LMMSE receiver that converges to an optimal linear receiver in the sense of minimizing the signal-to-noise-plus-interference ratio at the receiver output. If the adaptive filter portion is by-passed for some reason, for example to save power when experiencing good channel conditions, the receiver then functions as a conventional RAKE receiver.
The adaptive receiver has an inherent capability to (asymptotically) optimally perform beam forming, if the receiver has multiple antennas. Thus, if adaptive filtering is used in a multi-antenna receiver prior to a conventional multi-antenna RAKE, the overall receiver functions as an adaptive LMMSE receiver and performs beamforming in an optimal way. A RAKE receiver alone would perform this task suboptimally, unless additional algorithms are utilized.
The adaptive algorithm has a very simple structure. Because the reference vector used for the adaptation has only one non-zero element, the algorithm is actually less complex than the well-known LMS, which cannot be used in any case due to the lack of a reliable training sequence.
The adaptive algorithm is stable with mild requirements, and it converges to a known, optimal solution. For certain earlier ad hoc algorithms the stability was not guaranteed and they did not necessarily exhibit global convergence.
In case of a single receiver antenna, the adaptive filter may be symmetric with respect to a center filter tap, which can be utilized to make the adaptation speed of the algorithm faster.: Note should be made that the xe2x80x9ccenter tapxe2x80x9d is not necessarily the middle-most tap because, in general, one may have P+1+Q taps in the filter. Thus, the symmetry may hold with respect to the P+1""th filter tap. The filter is not symmetric if multiple antennas are used.
Disclosed herein is a general method to replace the operation of multiplying a received signal sample vector by an inverse covariance matrix of the input signal or by an inverse covariance matrix of the additional interference-plus-noise in the input signal (i.e., the input signal minus the desired signal). This type of matrix-vector multiplication is required in many well-known estimator structures as a part of the estimation algorithm (such as in the LMMSE estimator). The general method includes steps of: (a) estimating a row or a column of an inverse of a covariance matrix; and (b) using the elements of the estimate of the row or column vector as coefficients in a linear filter which is used to filter the input signal samples. In the presently preferred embodiment a received signal comprises a series of modulated pulse shapes, such as data symbol pulse shapes, each carrying an unknown parameter, such as a data symbol, and noise.
The filter coefficients form a vector w(i) which is an estimate of a row or a column of an inverse of the covariance matrix corresponding to a time interval i of the received signal. The estimation of w(i) can be based on an estimation of the signal covariance matrix, and then the use of an algorithm to compute the inverse of this matrix taking into account that only a row or column of the inverse is required. The step of filtering forms a filter output g(i) (scalar value). Consecutive filter outputs can be used to replace the vector that would be obtained by multiplying the received input signal vector by an inverse covariance matrix.
Also disclosed is a blind adaptive method to find the filter, whose coefficients given by vector w(i) converge to a row or column of the covariance matrix inverse. This method includes steps of: (a) initializing the linear filter using the best available a priori knowledge about the row or column of the inverse covariance matrix of interest; (b) generating a filter output g(i); and (c) adaptively updating the filter coefficients so that the filter converges towards a row or column of the inverse covariance matrix of interest.
In general, one may be interested in the inverse covariance matrix of the total received signal or in the inverse covariance matrix of the interference-plus-noise only (e.g. if the desired signal component is excluded or has first been subtracted from the total signal.
When the goal is to estimate a row or a column of an inverse covariance matrix, it may first be necessary to construct or estimate the covariance matrix itself. Further in this regard, as aspect of this invention is a method of using a row or a column of the inverse covariance matrix as a filter. This approach will, in most cases, reduce the computational complexity, which is an important consideration in power and resource-limited mobile electronics platforms, such as cellular telephones, PDAs, and personal communicators.
When the blind adaptive filter is used, the covariance matrix need not to be constructed or estimated separately to find a row or column of the inverse covariance matrix. In this case the adaptive filter adapts so that the filter coefficients (filter coefficients stacked into a vector) form an estimate of a row or column of the inverse covariance matrix.
Conventionally, one would first estimate the covariance matrix, then invert the covariance matrix, and then multiply the input signal vector by the inverse matrix. In accordance with the teachings of this invention, the output vector is estimated by the outputs of a single adaptive filter.
Note is made of the fact that the adaptive filter itself does not produce LMMSE estimates. The LMMSE estimates are produced only after the adaptative filter is followed by a filter matched to the pulse shape of the unknown parameter carrier by the received signal. Another condition is that the estimation be made of a row or column of the inverse (total) covariance matrix, and not of the inverse interference-plus-noise covariance matrix. The adaptive filter described herein may be considered to be a multi-purpose filter which is applied to LMMSE estimation, as an example.
A further step of the method applies the result (filter outputs) to a separate filter matched to a pulse shape of the unknown parameter to be estimated. These two filter together then form an adaptive LMMSE estimator of the unknown parameter. In a presently preferred embodiment the received signal is transmitted from a base station (BS) of a wireless network as a WCDMA signal, and the matched filter is implemented as a RAKE receiver that performs multipath combining at a chip level, as well as single code correlation. In this case the unknown parameter is a data symbol that is transmitted through and received from a wireless channel, such as the WCDMA channel.
Also disclosed is a receiver for receiving a signal from a channel using at least one antenna, where the received signal contains a data signal. The receiver includes an input section, such as an analog to digital converter for sampling the received signal. The receiver further includes a blind adaptive filter, which processes the input samples and generates output samples for further processing, and which converges to a filter coefficient vector that is an estimate of a row or column of an inverse covariance matrix. A RAKE receiver is preferably coupled to the output of the adaptive filter and performs multipath combining at the chip level in combination with a single code correlator.
In these embodiments the RAKE receiver can also be implemented so that it first despreads the multipaths using a code correlator bank, and then performs multipath combining at the symbol level using the correlator outputs.
Overall, the adaptive filter with the described post-processing (pulse shape matched filtering, e.g., a RAKE receiver) functions as an adaptive LMMSE filter that operates without a training sequence. It is shown that the filter coefficients of the adaptive filter converge to a (P+1)""th column or a row of the inverted covariance matrix (Crr(i))xe2x88x921, making complex matrix inversion unnecessary to perform.
This invention provides, for estimation or other purposes, that the required multiplication of an input signal vector by an inverse covariance matrix (total signal covariance matrix or interference-plus-noise covariance matrix) is replaced by linear filtering, where the elements (directly computed or estimated elements) of a row or a column of the inverse covariance matrix corresponding to time instant i are used as filter coefficients. The filter outputs form a vector g(i) that is estimated element by element using the linear filter. Vector g(i) can be used to replace the vector that would have been obtained by directly multiplying the signal vector by the inverse covariance matrix.
The teachings of this invention are not restricted to any specific estimation method (for example, to LMMSE, Maximum Likelihood (ML), etc.), and the filtering need not be adaptive at this general level. This general method may need the actual covariance matrix to be accurately constructed or estimated to be able to estimate a row or column of the inverse matrix, but not necessarily. In that only one row or column is required, a significant reduction in complexity can be obtained.
The invention further provides an extension of the foregoing by applying the novel adaptive filters so that the filter w(i) converges or closely converges to a row or column of the required inverse covariance matrix.
The following two cases can be distinguished. First, if a total signal covariance matrix is required (as in the case of linear minimum MSE, LMMSE, estimation), the input signal of the adaptive filter is the total signal (desired signal plus interference plus noise), and the filter outputs are used to generate output vector g(i). Second, if a noise covariance matrix is required (as for maximum likelihood, ML, estimation), the input signal to the filter is the interference plus noise signal, with the desired signal excluded. This is possible to achieve, for example, when the desired signal is known during a pilot signal period, and can thus be subtracted from the total signal. When the required filter has been found through adaptation, this filter can then be used to replace the required operation of inverting the covariance matrix and multiplying by the input signal vector (also including the desired signal) or some other signal vector by the inverse covariance matrix.
The filter outputs generated in accordance with the foregoing two cases are then employed to estimate unknown parameters, for example, as in LMMSE estimation, by decoupling the adaptive filter with a filter matched to the pulse shape of the unknown parameter carried by the received, sampled signal.